Extensions 1→N→G→Q→1 with N=C₂₀ and Q=C₂⁴

Direct product G=N×Q with N=C₂₀ and Q=C₂⁴

		d	ρ	Label	ID
C₂⁴×C₂₀		320		C2^4xC20	320,1628

Semidirect products G=N:Q with N=C₂₀ and Q=C₂⁴

extension	φ:Q→Aut N	d	Label	ID
C₂₀⋊C₂⁴ = C₂²×D₄×D₅	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80	C20:C2^4	320,1612
C₂₀⋊₂C₂⁴ = C₂³×D₂₀	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	160	C20:2C2^4	320,1610
C₂₀⋊₃C₂⁴ = D₅×C₂³×C₄	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	160	C20:3C2^4	320,1609
C₂₀⋊₄C₂⁴ = D₄×C₂²×C₁₀	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	160	C20:4C2^4	320,1629

Non-split extensions G=N.Q with N=C₂₀ and Q=C₂⁴

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀.₁C₂⁴ = C₂×D₅×D₈	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80		C20.1C2^4	320,1426
C₂₀.₂C₂⁴ = C₂×D₈⋊D₅	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80		C20.2C2^4	320,1427
C₂₀.₃C₂⁴ = C₂×D₈⋊₃D₅	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	160		C20.3C2^4	320,1428
C₂₀.₄C₂⁴ = D₈⋊₁₃D₁₀	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80	4	C20.4C2^4	320,1429
C₂₀.₅C₂⁴ = C₂×D₅×SD₁₆	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80		C20.5C2^4	320,1430
C₂₀.₆C₂⁴ = C₂×D₄₀⋊C₂	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80		C20.6C2^4	320,1431
C₂₀.₇C₂⁴ = C₂×SD₁₆⋊D₅	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	160		C20.7C2^4	320,1432
C₂₀.₈C₂⁴ = C₂×SD₁₆⋊₃D₅	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	160		C20.8C2^4	320,1433
C₂₀.₉C₂⁴ = D₂₀.₂₉D₄	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80	4	C20.9C2^4	320,1434
C₂₀.₁₀C₂⁴ = C₂×D₅×Q₁₆	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	160		C20.10C2^4	320,1435
C₂₀.₁₁C₂⁴ = C₂×Q₁₆⋊D₅	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	160		C20.11C2^4	320,1436
C₂₀.₁₂C₂⁴ = C₂×Q₈.D₁₀	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	160		C20.12C2^4	320,1437
C₂₀.₁₃C₂⁴ = D₂₀.₃₀D₄	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	160	4	C20.13C2^4	320,1438
C₂₀.₁₄C₂⁴ = D₅×C₄○D₈	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80	4	C20.14C2^4	320,1439
C₂₀.₁₅C₂⁴ = Q₁₆⋊D₁₀	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80	4	C20.15C2^4	320,1440
C₂₀.₁₆C₂⁴ = D₈⋊₁₅D₁₀	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80	4+	C20.16C2^4	320,1441
C₂₀.₁₇C₂⁴ = D₈⋊₁₁D₁₀	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80	4	C20.17C2^4	320,1442
C₂₀.₁₈C₂⁴ = D₂₀.₄₇D₄	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	160	4-	C20.18C2^4	320,1443
C₂₀.₁₉C₂⁴ = D₅×C₈⋊C₂²	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	40	8+	C20.19C2^4	320,1444
C₂₀.₂₀C₂⁴ = SD₁₆⋊D₁₀	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80	8-	C20.20C2^4	320,1445
C₂₀.₂₁C₂⁴ = D₈⋊₅D₁₀	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80	8+	C20.21C2^4	320,1446
C₂₀.₂₂C₂⁴ = D₈⋊₆D₁₀	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80	8-	C20.22C2^4	320,1447
C₂₀.₂₃C₂⁴ = D₅×C₈.C₂²	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80	8-	C20.23C2^4	320,1448
C₂₀.₂₄C₂⁴ = D₄₀⋊C₂²	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80	8+	C20.24C2^4	320,1449
C₂₀.₂₅C₂⁴ = C₄₀.C₂³	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80	8+	C20.25C2^4	320,1450
C₂₀.₂₆C₂⁴ = D₂₀.₄₄D₄	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	160	8-	C20.26C2^4	320,1451
C₂₀.₂₇C₂⁴ = C₂²×D₄⋊D₅	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	160		C20.27C2^4	320,1464
C₂₀.₂₈C₂⁴ = C₂×D₄.D₁₀	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80		C20.28C2^4	320,1465
C₂₀.₂₉C₂⁴ = C₂²×D₄.D₅	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	160		C20.29C2^4	320,1466
C₂₀.₃₀C₂⁴ = C₂²×Q₈⋊D₅	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	160		C20.30C2^4	320,1479
C₂₀.₃₁C₂⁴ = C₂×C₂₀.C₂³	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	160		C20.31C2^4	320,1480
C₂₀.₃₂C₂⁴ = C₂²×C₅⋊Q₁₆	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	320		C20.32C2^4	320,1481
C₂₀.₃₃C₂⁴ = C₂×D₄⋊D₁₀	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80		C20.33C2^4	320,1492
C₂₀.₃₄C₂⁴ = C₂×D₄.₈D₁₀	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	160		C20.34C2^4	320,1493
C₂₀.₃₅C₂⁴ = C₂₀.C₂⁴	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80	4	C20.35C2^4	320,1494
C₂₀.₃₆C₂⁴ = C₂×D₄.₉D₁₀	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	160		C20.36C2^4	320,1495
C₂₀.₃₇C₂⁴ = D₂₀.₃₂C₂³	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80	8+	C20.37C2^4	320,1507
C₂₀.₃₈C₂⁴ = D₂₀.₃₃C₂³	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80	8-	C20.38C2^4	320,1508
C₂₀.₃₉C₂⁴ = D₂₀.₃₄C₂³	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80	8+	C20.39C2^4	320,1509
C₂₀.₄₀C₂⁴ = D₂₀.₃₅C₂³	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	160	8-	C20.40C2^4	320,1510
C₂₀.₄₁C₂⁴ = C₂²×D₄⋊₂D₅	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	160		C20.41C2^4	320,1613
C₂₀.₄₂C₂⁴ = C₂×D₄⋊₆D₁₀	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80		C20.42C2^4	320,1614
C₂₀.₄₃C₂⁴ = C₂²×Q₈×D₅	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	160		C20.43C2^4	320,1615
C₂₀.₄₄C₂⁴ = C₂²×Q₈⋊₂D₅	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	160		C20.44C2^4	320,1616
C₂₀.₄₅C₂⁴ = C₂×Q₈.₁₀D₁₀	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	160		C20.45C2^4	320,1617
C₂₀.₄₆C₂⁴ = C₂×D₅×C₄○D₄	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80		C20.46C2^4	320,1618
C₂₀.₄₇C₂⁴ = C₂×D₄⋊₈D₁₀	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80		C20.47C2^4	320,1619
C₂₀.₄₈C₂⁴ = C₂×D₄.₁₀D₁₀	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	160		C20.48C2^4	320,1620
C₂₀.₄₉C₂⁴ = C₁₀.C₂⁵	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80	4	C20.49C2^4	320,1621
C₂₀.₅₀C₂⁴ = D₅×2₊¹⁺⁴	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	40	8+	C20.50C2^4	320,1622
C₂₀.₅₁C₂⁴ = D₂₀.₃₇C₂³	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80	8-	C20.51C2^4	320,1623
C₂₀.₅₂C₂⁴ = D₅×2_-¹⁺⁴	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80	8-	C20.52C2^4	320,1624
C₂₀.₅₃C₂⁴ = D₂₀.₃₉C₂³	φ: C₂⁴/C₂² → C₂² ⊆ Aut C₂₀	80	8+	C20.53C2^4	320,1625
C₂₀.₅₄C₂⁴ = C₂²×C₄₀⋊C₂	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	160		C20.54C2^4	320,1411
C₂₀.₅₅C₂⁴ = C₂²×D₄₀	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	160		C20.55C2^4	320,1412
C₂₀.₅₆C₂⁴ = C₂×D₄₀⋊₇C₂	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	160		C20.56C2^4	320,1413
C₂₀.₅₇C₂⁴ = C₂²×Dic₂₀	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	320		C20.57C2^4	320,1414
C₂₀.₅₈C₂⁴ = C₂×C₈⋊D₁₀	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	80		C20.58C2^4	320,1418
C₂₀.₅₉C₂⁴ = C₂×C₈.D₁₀	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	160		C20.59C2^4	320,1419
C₂₀.₆₀C₂⁴ = C₄₀.₉C₂³	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	80	4	C20.60C2^4	320,1420
C₂₀.₆₁C₂⁴ = D₄.₁₁D₂₀	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	80	4	C20.61C2^4	320,1423
C₂₀.₆₂C₂⁴ = D₄.₁₂D₂₀	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	80	4+	C20.62C2^4	320,1424
C₂₀.₆₃C₂⁴ = D₄.₁₃D₂₀	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	160	4-	C20.63C2^4	320,1425
C₂₀.₆₄C₂⁴ = C₂³×Dic₁₀	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	320		C20.64C2^4	320,1608
C₂₀.₆₅C₂⁴ = D₅×C₂²×C₈	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	160		C20.65C2^4	320,1408
C₂₀.₆₆C₂⁴ = C₂²×C₈⋊D₅	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	160		C20.66C2^4	320,1409
C₂₀.₆₇C₂⁴ = C₂×D₂₀.₃C₄	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	160		C20.67C2^4	320,1410
C₂₀.₆₈C₂⁴ = C₂×D₅×M₄(2)	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	80		C20.68C2^4	320,1415
C₂₀.₆₉C₂⁴ = C₂×D₂₀.₂C₄	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	160		C20.69C2^4	320,1416
C₂₀.₇₀C₂⁴ = C₄₀.₄₇C₂³	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	80	4	C20.70C2^4	320,1417
C₂₀.₇₁C₂⁴ = D₅×C₈○D₄	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	80	4	C20.71C2^4	320,1421
C₂₀.₇₂C₂⁴ = C₂₀.₇₂C₂⁴	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	80	4	C20.72C2^4	320,1422
C₂₀.₇₃C₂⁴ = C₂³×C₅⋊₂C₈	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	320		C20.73C2^4	320,1452
C₂₀.₇₄C₂⁴ = C₂²×C₄.Dic₅	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	160		C20.74C2^4	320,1453
C₂₀.₇₅C₂⁴ = C₂×D₄.Dic₅	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	160		C20.75C2^4	320,1490
C₂₀.₇₆C₂⁴ = C₂₀.₇₆C₂⁴	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	80	4	C20.76C2^4	320,1491
C₂₀.₇₇C₂⁴ = C₂²×C₄○D₂₀	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	160		C20.77C2^4	320,1611
C₂₀.₇₈C₂⁴ = D₈×C₂×C₁₀	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	160		C20.78C2^4	320,1571
C₂₀.₇₉C₂⁴ = SD₁₆×C₂×C₁₀	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	160		C20.79C2^4	320,1572
C₂₀.₈₀C₂⁴ = Q₁₆×C₂×C₁₀	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	320		C20.80C2^4	320,1573
C₂₀.₈₁C₂⁴ = C₁₀×C₄○D₈	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	160		C20.81C2^4	320,1574
C₂₀.₈₂C₂⁴ = C₁₀×C₈⋊C₂²	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	80		C20.82C2^4	320,1575
C₂₀.₈₃C₂⁴ = C₁₀×C₈.C₂²	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	160		C20.83C2^4	320,1576
C₂₀.₈₄C₂⁴ = C₅×D₈⋊C₂²	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	80	4	C20.84C2^4	320,1577
C₂₀.₈₅C₂⁴ = C₅×D₄○D₈	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	80	4	C20.85C2^4	320,1578
C₂₀.₈₆C₂⁴ = C₅×D₄○SD₁₆	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	80	4	C20.86C2^4	320,1579
C₂₀.₈₇C₂⁴ = C₅×Q₈○D₈	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	160	4	C20.87C2^4	320,1580
C₂₀.₈₈C₂⁴ = Q₈×C₂²×C₁₀	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	320		C20.88C2^4	320,1630
C₂₀.₈₉C₂⁴ = C₄○D₄×C₂×C₁₀	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	160		C20.89C2^4	320,1631
C₂₀.₉₀C₂⁴ = C₁₀×2₊¹⁺⁴	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	80		C20.90C2^4	320,1632
C₂₀.₉₁C₂⁴ = C₁₀×2_-¹⁺⁴	φ: C₂⁴/C₂³ → C₂ ⊆ Aut C₂₀	160		C20.91C2^4	320,1633
C₂₀.₉₂C₂⁴ = M₄(2)×C₂×C₁₀	central extension (φ=1)	160		C20.92C2^4	320,1568
C₂₀.₉₃C₂⁴ = C₁₀×C₈○D₄	central extension (φ=1)	160		C20.93C2^4	320,1569
C₂₀.₉₄C₂⁴ = C₅×Q₈○M₄(2)	central extension (φ=1)	80	4	C20.94C2^4	320,1570
C₂₀.₉₅C₂⁴ = C₅×C₂.C₂⁵	central extension (φ=1)	80	4	C20.95C2^4	320,1634

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Extensions 1→N→G→Q→1 with N=C20 and Q=C24

Extensions 1→N→G→Q→1 with N=C₂₀ and Q=C₂⁴